The basic task in BART is to pump up a virtual balloon using on-screen buttons. With each pump, the balloon grows a bit and the player gains a point, which are linked to monetary rewards — the more the players pump up the balloons, the higher their payoff. The maximum size of a balloon is reached after 128 pumps. The risk is introduced through a random, uniformly distributed, point of explosion for each balloon with the average and median explosion point at 64 pumps. The optimal strategy to maximise payoff is to perform 64 pumps. Each participant repeats this 30 times.
BART tasks have been commonly used in psychology research to assess risk-taking behavior. A meta-analysis of 22 studies which used the BART task found that the average number of pumps (averaged across conditions) to vary between 24.60 to 44.10 (out of 128 total possible pumps), with a weighted standard deviation of 5.93. This means that based on prior studies, on average, participants in the BART task are most likely to be risk-averse.
The data will be analysed using a poisson regression model: the outcome variable will be the number of pumps by the participant, and the predictor will be a (categorical) dummy variable indicating which condition the participant is in.
\[ pumps_i \sim Poisson(\lambda_i) \\ log(\lambda_i) \sim \alpha + \beta \times condition_i \] where, \(condition_i\) has two levels: 0 for the constrictive condition, and 1 for the expansive condition.
Use the following visualizations to specify your final choice of priors which you would use to analyse the data. Please specify one prior distribution for each parameter. It can be from either distribution family. You do not need to specify an exact value to the hundredth decimal point — please specify an approximate value that you think is suitable.
Select your choice of priors for the intercept parameter, \(\alpha\):
Constrictive
Expansive
Select your choice of priors for the mean difference parameter, \(\beta\):
Constrictive
Expansive